Elliptic curves over $\Q$ of conductor 704

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Label	Cremona label	Class	Cremona class	Class size	Class degree	Conductor	Discriminant	Rank	Torsion	$\textrm{End}^0(E_{\overline\Q})$	CM	Sato-Tate	Semistable	Potentially good	Nonmax $\ell$	$\ell$-adic images	mod-$\ell$ images	Adelic level	Adelic index	Adelic genus	Regulator	$Ш_{\textrm{an}}$	Ш primes	Integral points	Modular degree	Faltings height	j-invariant	$abc$ quality	Szpiro ratio	Weierstrass coefficients	Weierstrass equation	mod-$m$ images	MW-generators
704.a1	704l1	704.a	704l	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11^{3} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$132$	$12$	$1$	$0.297417219$	$1$		$4$	$96$	$-0.374511$	$13824/1331$	$1.17246$	$2.86745$	$[0, 0, 0, 2, -14]$	\(y^2=x^3+2x-14\)	3.3.0.a.1, 12.6.0.d.1, 22.2.0.a.1, 66.6.1.a.1, 132.12.1.?	$[(5, 11)]$
704.b1	704i1	704.b	704i	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{14} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$128$	$-0.282638$	$-27648/11$	$0.78666$	$3.11961$	$[0, 0, 0, -16, -32]$	\(y^2=x^3-16x-32\)	22.2.0.a.1	$[]$
704.c1	704k3	704.c	704k	$3$	$25$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.2	5B.4.2	$2200$	$1200$	$37$	$0.915095465$	$1$		$0$	$400$	$0.843283$	$-52893159101157376/11$	$1.09296$	$6.50715$	$[0, -1, 0, -31281, 2139919]$	\(y^2=x^3-x^2-31281x+2139919\)	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 40.24.0-5.a.2.1, 110.24.1.?, $\ldots$	$[(922/3, 1/3)]$
704.c2	704k2	704.c	704k	$3$	$25$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.60.0.1	5Cs.4.1	$2200$	$1200$	$37$	$0.183019093$	$1$		$4$	$80$	$0.038564$	$-122023936/161051$	$1.01300$	$3.65525$	$[0, -1, 0, -41, 199]$	\(y^2=x^3-x^2-41x+199\)	5.60.0.a.1, 22.2.0.a.1, 40.120.0-5.a.1.1, 110.120.5.?, 275.300.12.?, $\ldots$	$[(2, 11)]$
704.c3	704k1	704.c	704k	$3$	$25$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.1	5B.4.1	$2200$	$1200$	$37$	$0.915095465$	$1$		$2$	$16$	$-0.766155$	$-4096/11$	$0.82546$	$2.16671$	$[0, -1, 0, -1, -1]$	\(y^2=x^3-x^2-x-1\)	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 40.24.0-5.a.1.1, 110.24.1.?, $\ldots$	$[(2, 1)]$
704.d1	704g1	704.d	704g	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$32$	$-0.600497$	$-2515456/11$	$0.85957$	$2.88318$	$[0, -1, 0, -11, -11]$	\(y^2=x^3-x^2-11x-11\)	22.2.0.a.1	$[]$
704.e1	704b1	704.e	704b	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$0.527945940$	$1$		$2$	$32$	$-0.773302$	$512/11$	$0.81074$	$2.13278$	$[0, -1, 0, 1, 1]$	\(y^2=x^3-x^2+x+1\)	22.2.0.a.1	$[(0, 1)]$
704.f1	704d2	704.f	704d	$2$	$3$	\( 2^{6} \cdot 11 \)	\( - 2^{14} \cdot 11^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$264$	$16$	$0$	$1$	$1$		$0$	$192$	$0.243586$	$-199794688/1331$	$0.99506$	$4.39672$	$[0, -1, 0, -309, -2003]$	\(y^2=x^3-x^2-309x-2003\)	3.4.0.a.1, 22.2.0.a.1, 24.8.0-3.a.1.1, 66.8.0.a.1, 264.16.0.?	$[]$
704.f2	704d1	704.f	704d	$2$	$3$	\( 2^{6} \cdot 11 \)	\( - 2^{14} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$264$	$16$	$0$	$1$	$1$		$0$	$64$	$-0.305720$	$8192/11$	$0.84294$	$2.89667$	$[0, -1, 0, 11, -19]$	\(y^2=x^3-x^2+11x-19\)	3.4.0.a.1, 22.2.0.a.1, 24.8.0-3.a.1.2, 66.8.0.a.1, 264.16.0.?	$[]$
704.g1	704j1	704.g	704j	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$0.440106483$	$1$		$2$	$32$	$-0.600497$	$-2515456/11$	$0.85957$	$2.88318$	$[0, 1, 0, -11, 11]$	\(y^2=x^3+x^2-11x+11\)	22.2.0.a.1	$[(2, 1)]$
704.h1	704a3	704.h	704a	$3$	$25$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.2	5B.4.2	$2200$	$1200$	$37$	$12.68007523$	$1$		$0$	$400$	$0.843283$	$-52893159101157376/11$	$1.09296$	$6.50715$	$[0, 1, 0, -31281, -2139919]$	\(y^2=x^3+x^2-31281x-2139919\)	5.12.0.a.2, 22.2.0.a.1, 25.60.0.a.2, 40.24.0-5.a.2.3, 110.24.1.?, $\ldots$	$[(267088/23, 128202697/23)]$
704.h2	704a2	704.h	704a	$3$	$25$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11^{5} \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	5.60.0.1	5Cs.4.1	$2200$	$1200$	$37$	$2.536015047$	$1$		$2$	$80$	$0.038564$	$-122023936/161051$	$1.01300$	$3.65525$	$[0, 1, 0, -41, -199]$	\(y^2=x^3+x^2-41x-199\)	5.60.0.a.1, 22.2.0.a.1, 40.120.0-5.a.1.3, 110.120.5.?, 275.300.12.?, $\ldots$	$[(8, 7)]$
704.h3	704a1	704.h	704a	$3$	$25$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$1$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$5$	25.60.0.1	5B.4.1	$2200$	$1200$	$37$	$0.507203009$	$1$		$2$	$16$	$-0.766155$	$-4096/11$	$0.82546$	$2.16671$	$[0, 1, 0, -1, 1]$	\(y^2=x^3+x^2-x+1\)	5.12.0.a.1, 22.2.0.a.1, 25.60.0.a.1, 40.24.0-5.a.1.3, 110.24.1.?, $\ldots$	$[(0, 1)]$
704.i1	704f2	704.i	704f	$2$	$3$	\( 2^{6} \cdot 11 \)	\( - 2^{14} \cdot 11^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$264$	$16$	$0$	$1$	$1$		$0$	$192$	$0.243586$	$-199794688/1331$	$0.99506$	$4.39672$	$[0, 1, 0, -309, 2003]$	\(y^2=x^3+x^2-309x+2003\)	3.4.0.a.1, 22.2.0.a.1, 24.8.0-3.a.1.3, 66.8.0.a.1, 264.16.0.?	$[]$
704.i2	704f1	704.i	704f	$2$	$3$	\( 2^{6} \cdot 11 \)	\( - 2^{14} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.4.0.1	3B	$264$	$16$	$0$	$1$	$1$		$0$	$64$	$-0.305720$	$8192/11$	$0.84294$	$2.89667$	$[0, 1, 0, 11, 19]$	\(y^2=x^3+x^2+11x+19\)	3.4.0.a.1, 22.2.0.a.1, 24.8.0-3.a.1.4, 66.8.0.a.1, 264.16.0.?	$[]$
704.j1	704c1	704.j	704c	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$32$	$-0.773302$	$512/11$	$0.81074$	$2.13278$	$[0, 1, 0, 1, -1]$	\(y^2=x^3+x^2+x-1\)	22.2.0.a.1	$[]$
704.k1	704h1	704.k	704h	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{6} \cdot 11^{3} \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$			$3$	3.3.0.1	3Nn	$132$	$12$	$1$	$1$	$1$		$0$	$96$	$-0.374511$	$13824/1331$	$1.17246$	$2.86745$	$[0, 0, 0, 2, 14]$	\(y^2=x^3+2x+14\)	3.3.0.a.1, 12.6.0.d.1, 22.2.0.a.1, 66.6.1.a.1, 132.12.1.?	$[]$
704.l1	704e1	704.l	704e	$1$	$1$	\( 2^{6} \cdot 11 \)	\( - 2^{14} \cdot 11 \)	$0$	$\mathsf{trivial}$	$\Q$		$\mathrm{SU}(2)$						$22$	$2$	$0$	$1$	$1$		$0$	$128$	$-0.282638$	$-27648/11$	$0.78666$	$3.11961$	$[0, 0, 0, -16, 32]$	\(y^2=x^3-16x+32\)	22.2.0.a.1	$[]$

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